Estimation of Large Correlation Matrix with Shrinking Methods

Abstract

An exact estimation of the true correlation matrix is highly desirable in many applications. In practice there will always be an estimation error which, however, can be not only minimized using the shrinking approach but also an invertible correlation matrix can be calculated when there are fewer observations than assets. We compare several shrinking methods regarding their correlation matrix estimation using several data generating processes. We calculate the distance of the estimator to the true matrix and check, if improvements transfer to economic improvement, measured by the Sharpe ratio. Firstly, we find that a more accurate estimation of the covariance matrix leads to a better estimation of the correlation matrix and secondly, better estimations of the correlation matrix lead to significant economic improvements. Although each shrinking estimator performs differently regarding the shape of the return distribution, the general usage of shrinking estimators leads to a better estimation of the correlation matrix than the standard estimator.